Just to clarify: The rim size as such has no effect on snow performance, the latter is directly related to the tire width (= 1st number in the tire dimension) and of course the winter specific characteristics of the tire thread and compounds. As a rule of thumb, narrower tires of the same tire model will generally perform better on snow and slush, however such narrower tire dimensions will rather be available on smaller rim sizes. That's why many have smaller winter rims.

BTW I have 20" in summer and 18" in winter (same package Gilgorm mentioned above)